Outwith the context of clinical trial design, a great deal of research has addressed optimisation problems where the evaluation of a solution is a computationally demanding, or expensive, operation [1]}, [2]}. One approach addresses the problem by substituting the expensive function with a mathematical approximation known as a surrogate model. The surrogate model is then used to make predictions about the true function for different values of design parameters, with these predictions informing which point should be evaluated next. The information obtained from this evaluation is used to update the surrogate model, thus improving the predictions available at the next iteration. One class of surrogate model is Gaussian process (GP) regression. Also known as Kriging and having its roots in geostatistics [3]}, GP models are spatial interpolators which are computationally tractable [4]} and can be fitted using robust and freely available software [5]}. A GP surrogate model provides not only a prediction of the true function value at any point, but also a measure of uncertainty in this prediction. This property is exploited by the benchmark Efficient Global Optimisation (EGO) algorithm [6]}, allowing the next point in the search to be chosen in a way that formally balances the potential benefits of exploitation (searching around areas already known to be promising) and exploration (searching in areas of high uncertainty). Although EGO was originally proposed for unconstrained optimisation of expensive objective functions with deterministic output, various proposals have extended it to incorporate the expensive constraints [7]}, multiple objectives [8]}, and stochastic outputs [9]} that feature in complex SSD problems.
